A Test of Steady State Erosion Models

Here we ask the question: how well is the erosion of particle beds in vessels with curved bottoms at industrial scale flow rates represented by models of radial wall jets traversing flat surfaces using the critical shear stress for erosion from the Shields diagram? This mathematical construction has been used successfully to predict the functional forms for the extent of erosion with time using two dimensionless fitting parameters (Pease, et al., 2017). However, the direct prediction of the curves without fitting and scaling has not been tested quantitatively. Here we evaluate the radial wall jet models of Poreh, et al., (1967) and Rajaratnam (1976) and the expressions for the Shields diagram by Paphitis (2001) and Cao, Pender, and Meng (2006). The use of two models for each element accounts for uncertainty in model selection. The data selected to benchmark these models was obtained in a geometrically scaled version of an industrial scale mixing vessel with 12 jets arrayed in a double ring configuration (Meyer, et al., 2012). These particular jets were operated continuously with observations at steady-state, providing a direct comparison between the long-time erosion fronts and these proposed long-time solutions (i.e., where the applied shear stress equals the critical shear stress for erosion) without interference from transients or parameters that affect transients (e.g., the particle bed thickness). We find experimentally that the extent of the erosion depends significantly on the vessel curvature. Even so, we also find that all of these formulations significantly over predict the extent of erosion observed experimentally. A discussion of model features that may be modified to revise the theory into quantitative agreement is presented.